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1 B A S I C M A T H A Self-Tutorial by Luis Anthony Ast Professional Mathematics Tutor LESSON 7: UNITS OF MEASUREMENT Copyright 2006 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage or retrieval system, without permission in writing of the author. may be sent to: Luis-Ast@VideoMathTutor.com

2 UNITS OF TIME The basic unit of time is the Second, defined as 9,192,631,770 oscillations of the atom of cesium minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 fortnight = 2 weeks = 14 days (or nights) 1 month 30 days 4 weeks 1 year = 365 days = 52 weeks = 12 months 1 leap year = 366 days 1 decade = 10 years 1 century = 100 years 1 millennium = 1000 years ABBREVIATIONS 2

3 UNITS OF LENGTH METRIC SYSTEM The Meter is the basic unit of measurement of length. It is defined as the total distance a beam of light would travel in of a second. To get an idea of this length, it is approximately equal to just over times the width of a letter size page of paper: Page ===== ===== Page ===== ===== Page ===== ===== Page ===== ===== Page ===== ===== 1 meter Assuming the following represents a meter: 1 decimeter = meter A better view of this portion is 1 decimeter 1 centimeter = decimeter = meter 3

4 1 millimeter = centimeter = decimeter = meter Another look at this: Keep in mind: 1 meter = Here are units larger than a meter: 1 decameter = 10 meters 1 hectometer = 100 meters 4

5 U.S. CUSTOMARY SYSTEM = Imperial Units (United Kingdom) are NOT covered in this lesson, only the American System. Also, not all units are discussed, just the more typical ones. The Yard is the basic unit of measurement of length. It is defined as meters. 1 inch = foot = yard 1 foot = 12 inches = yard 1 yard = 3 feet = 36 inches 1 mile = 1760 yards = 5280 feet CONVERSIONS Here are the most typical formulas to convert units from one system to another. Most values are approximate, unless otherwise noted. I will provide one example of how to use them. This is meant more as a reference. More manipulations of units are done in other Lessons centimeters = inches 2.54 inches = centimeters <exactly> meters = feet feet = meters <exactly> 5

6 meters = yards yards = meters <exactly> kilometers = miles miles = kilometers <exactly> ABBREVIATIONS EXAMPLE 1: Convert 38 inches into centimeters. SOLUTION: To convert inches to centimeters, we will use the formula: 2.54 inches = centimeters = The Answer is 96.52cm. 6

7 UNITS OF AREA METRIC SYSTEM The Square Meter is the basic unit of measurement of area. It is defined as a square whose sides are of length one meter. 1 meter 1 meter 1 square millimeter = square centimeter 1 square centimeter = square decimeter 1 square decimeter = square meter 7

8 Other units: 1 square decameter = 100 square meters 1 square hectometer = 100 square decameters 1 square kilometer = 100 square hectometers U.S. CUSTOMARY SYSTEM The Square Yard is the basic unit of measurement of area. It is defined as a square whose sides are of length one yard. 1 yard 1 square inch 1 yard 1 square inch 1 square foot = 144 square inches 1 square foot 1 square yard = 9 square feet = 1296 square inches 8

9 1 acre = 4840 square yards 1 square mile = 640 acres CONVERSIONS square centimeters = square inches square inches = square centimeters <exactly> square meters = square feet square feet = square meters square meters = square yards square yards = square meters square kilometers = square miles square miles = square kilometers ABBREVIATIONS 9

10 UNITS OF VOLUME METRIC SYSTEM The Cubic Meter is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one meter. 1 meter 1 meter 1 meter " 1 cubic millimeter = cubic centimeter 1 cubic centimeter = cubic decimeter 1 cubic decimeter = cubic meter 10

11 Other units: 1 cubic decameter = 1000 cubic meters 1 cubic hectometer = 1000 cubic decameters 1 cubic kilometer = 1000 cubic hectometers U.S. CUSTOMARY SYSTEM The Cubic Yard is the basic unit of measurement of volume. It is defined as a cube whose sides are of length one yard. 1 yard 1 yard 1 yard 1 cubic inch = cubic foot 1 cubic foot = 1728 cubic inches = cubic yard gallons 1 cubic yard = 27 cubic feet 4 feet 1 cord = feet = 128 cubic feet 8 feet 4 feet 11

12 CONVERSIONS cubic centimeters = cubic inches cubic inches = cubic centimeters <exactly> cubic meters = cubic feet cubic feet = cubic meters cubic meters = cubic yards cubic yards = cubic meters ABBREVIATIONS 12

13 UNITS OF MASS METRIC SYSTEM The Kilogram is the basic unit of measurement of mass. It is defined as the mass of a certain cylinder made of platinum iridium kept in Sèvres, France. It is called the International Prototype Kilogram. [ 1 milligram = gram 1 gram = kilogram 1 kilogram = 1000 grams 1 metric ton = 1000 kilograms = How I usually feel after a big lunch! U.S. CUSTOMARY SYSTEM The Pound is the basic unit of measurement of mass. It is defined to be kilograms. <Exactly> 1 ounce = pound 1 pound = 16 ounces 1 ton = 2000 pounds <Also called the short ton> 13

14 CONVERSIONS grams = ounces ounces = grams kilograms = pounds pounds = kilograms <exactly> short tons = metric tons metric tons = short tons ABBREVIATIONS ounce = oz pound = lb <lower case of LB> 14

15 UNITS OF LIQUID CAPACITY METRIC SYSTEM The Liter is the basic unit of measurement of capacity (both liquid and dry). It is the volume of 1 kilogram of water under specific scientific conditions. 1 milliliter = liter = 1 cubic centimeter 1 liter = 1000 milliliters = 1 cubic decimeter 1 kiloliter = 1000 liters = 1 cubic meter U.S. CUSTOMARY SYSTEM The Gallon is the basic unit of measurement of liquid capacity. It is equal to 231 cubic inches. 1 drop = teaspoon = fluid ounce 1 teaspoon = tablespoon = 60 drops = fluid ounce 1 tablespoon = 3 teaspoons = fluid ounce = cup 15

16 1 fluid ounce = pint = quart = gallon 1 cup = pint = 8 fluid ounces 1 pint = quart = 16 fluid ounces 1 quart = gallon = 2 pints = 4 cups = 32 fluid ounces 1 gallon = 4 quarts = 128 fluid ounces CONVERSIONS liters = gallons gallons = liters <exactly> liters = quarts quarts = liters ABBREVIATIONS 16

17 UNITS OF DRY CAPACITY Same as liquid. METRIC SYSTEM U.S. CUSTOMARY SYSTEM The Bushel is the basic unit of measurement of dry capacity. It is equal to cubic inches. = Although the same names are used, liquid pints and quarts are NOT the same size as dry pints and quarts. 1 pint = quart 1 quart = 2 pints = peck 1 peck = 8 quarts = bushel 1 bushel = 4 pecks CONVERSIONS liters = dry pints dry pints = liters liters = dry quarts dry quarts = liters liters = pecks pecks = liters liters = bushels bushels = liters <exactly> 17

18 ABBREVIATIONS OTHER USEFUL INFORMATION SOME COUNTING UNITS 1 dozen = 12 (Abbreviation: dz) 1 baker s dozen = 13 1 score = 20 1 gross = 144 (12 dozens) (Abbreviation: gr) 1 ream = 500 (Abbreviation: rm) ANGLE MEASURE 1 second = minute 1 minute = degree 1 degree = of a circle SYMBOLS: Degree: Minute: Second: 1 degree = 1 18

19 1 right angle = 90 = of a circle 1 straight angle = 180 = of a circle A protractor is typically used to measure angles: 19

20 UNITS OF TEMPERATURE The Degree is used as the basic unit of temperature; however, there are several temperature scales commonly used. Two will be discussed here: Fahrenheit and Celsius. Degrees Fahrenheit: Math Symbol: F <Read: degrees Fahrenheit > 212 F Boiling point of water 180 degrees 32 F Freezing point of water Degrees Celsius: Math Symbol: C <Read: degrees Celsius > 100 C Boiling point of water 100 degrees 0 C Freezing point of water 20

21 If you are given degrees Celsius (C) and want degrees Fahrenheit (F), use this formula to convert the values: If you are given degrees Fahrenheit (F) and want degrees Celsius (C), use this formula to convert the values: Examples of these conversions will be done in another Lesson. END OF LESSON 7 21